Fuzzy Sub-Equality Algebras Based on Fuzzy Points

Mona Aaly Kologani; Mohammad Mohseni Takallo; Young Bae Jun; Rajab Ali Borzooei

doi:10.18778/0138-0680.2023.31

Authors

Mona Aaly Kologani Hatef Higher Education, Zahedan, Iran Author https://orcid.org/0000-0002-5234-2876
Mohammad Mohseni Takallo Shahid Beheshti University, Department of Mathematics, Faculty of Mathematical Sciences, Tehran, Iran Author
Young Bae Jun Gyeongsang National University, Department of Mathematics Education, Jinju, Korea Author https://orcid.org/0000-0002-0181-8969
Rajab Ali Borzooei Istinye University, Department of Mathematics, Faculty of Engineering and Natural Sciences, Istanbul, Turkiye; Shahid Beheshti University, Department of Mathematics, Faculty of Mathematical Sciences, Tehran, Iran Author https://orcid.org/0000-0001-7538-7885

DOI:

https://doi.org/10.18778/0138-0680.2023.31

Keywords:

equality algebra, fuzzy set, fuzzy point, fuzzy ideal, sub-equality algebras, \((\in, \in)\)-fuzzy sub-equality algebras, \((\in, \in\! \vee \, {q})\)-fuzzy sub-equality algebras, \((q, \in\! \vee \, {q})\)-fuzzy sub-equality algebras

Abstract

In this paper, by using the notion of fuzzy points and equality algebras, the notions of fuzzy point equality algebra, equality-subalgebra, and ideal were established. Some characterizations of fuzzy subalgebras were provided by using such concepts. We defined the concepts of \((\in, \in)\) and \((\in, \in\! \vee \, {q})\)-fuzzy ideals of equality algebras, discussed some properties, and found some equivalent definitions of them. In addition, we investigated the relation between different kinds of \((\alpha,\beta)\)-fuzzy subalgebras and \((\alpha,\beta)\)-fuzzy ideals on equality algebras. Also, by using the notion of \((\in, \in)\)-fuzzy ideal, we defined two equivalence relations on equality algebras and we introduced an order on classes of \(X\), and we proved that the set of all classes of \(X\) by these order is a poset.

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